How to project/imprint a texture using a mesh as its source
You can bake this. Give the texture mesh an emission material. Select the object, then the target object (SHIFT). 



In an image editor create a new texture (square, left)
Add an image texture node to the material of the target object,
select your new texture. It does not have to be connected to
anything, but make sure it's active (clicked on)
In the render settings tab, copy my settings.
Press Bake.